Berichte der Arbeitsgruppe Technomathematik (AGTM Report)
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- Boltzmann Equation (7)
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- radiative heat transfer (1)
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- rate of convergence (1)
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- reconstruction formula (1)
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- structure tensor (1)
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- windowed Fourier transform (1)
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Faculty / Organisational entity
225
Wir beschreiben eine Methode zur Approximation von Spannungsgradienten aus diskreten Spannungsdaten. Eine herkömmliche Diskretisierung der Ableitungen aus Funktionswerten führt zu Stabilitätsproblemen, weswegen eine Möglichkeit zur Kontrolle der Ableitungen notwendig ist (Regularisierung). Wir bestimmen zunächst das Funktional der potentiellen Energie und führen zusätzlich ein Fehlerfunktional ein, das die Anpassung an die vorgegebenen diskreten Werte ermöglicht. Durch Gewichtung der beiden Funktionale und Minimierung des Gesamtfunktionals erhält man den gewünschten Ausgleich zwischen der Fehlerkontrolle beim Ableiten einerseits und Kontrolle der Fehler bei den Randwerten andererseits.
172
Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems
(1999)
Some inequalities for the Boltzmann collision integral are proved. These inequalities can be considered as a generalization of the well-known Povzner inequality. The inequalities are used to obtain estimates of moments of solution to the spatially homogeneous Boltzmann equation for a wide class of intermolecular forces. We obtained simple necessary and sufficient conditions (on the potential) for the uniform boundedness of all moments. For potentials with compact support the following statement is proved. .....
122
The Boltzmann equation solutions are considered for the small Knudsen number. The main attention is devoted to certain deviations from the classical Navier-Stokes description. The equations for the quasistationary slow flows are derived. These equations do not contain the Knudsen number and provide in this sense a limiting description of hydrodynamical variables. Two well-known special cases are also indicated. In the isothermal case the equations are equivalent to the incompressible Navier-Stokes equations, in stationary case they coincide with the equations of slow non-isothermal flows. It is shown that the derived equations possess all principal properties of the Boltzmann equation on contrast to the Burnett equations. In one dimension the equations reduce to the nonlinear diffusion equations, being exactly solvable for Maxwell molecules. Multidimensional stationary heat-transfer problems are also discussed. It is shown that one can expect an essential difference between the Boltzmann equaiton solution in the limit of the continuous media and the corresponding solution of the Navier-Stokes equations.
124
99
Exact Solutions of Discrete Kinetic Models and Stationary Problems for the Plane Broadwell Model
(1993)
123
The paper presents some approximation methods for the Boltzmann equation. In the first part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution function as long as the mass conservation is strictly fulfilled. For a simple model Boltzmann equation some unexpected features of the implicit scheme and the corresponding iteration process are clarified. In the second part a new iteration algorithm is proposed which should be used for the stationary Boltzmann equation. The realization of the method is very similar to the standard splitting algorithms except some new stochastic elements.
49
On the Moving Preisach Model
(1990)
33
35